基于语言判断矩阵的信息不完全的群决策方法

Group decision-making method with incomplete certain information based on linguistic judgement matrices

针对方案间的比较信息为确定语言等级或位于两个连续语言等级之间,甚至缺失,以及决策者权系数信息不完全确定的群决策问题,提出一种基于证据推理和二元语义的群决策方法。该方法根据决策者的原始评价矩阵信息得到属于语言等级的信任度,利用证据推理算法得到各方案在各语言等级下的信任度,将其转化为二元语义形式,根据决策者权系数的不完全确定信息和二元语义的距离等构建非线性规划模型,并利用改进的粒子群算法进行求解,根据求解结果得到方案集的一个排序。最后实例说明了该方法的可行性和有效性。

As concerning group decision-making problems with linguistic assessment information, a new method based on evidential reasoning （ER） and two-tuple is proposed, in which the decision-makers＇ preference information may takes the form of linguistic grade ,or may be between two continuous linguistic grade ,or may be not given, and the criteria of the decision-makers may be incomplete certain. The belief degrees that one alternative over another alternative is assessed to each linguistic grade are obtained according to the original reciprocal judgment matrix given by decision-makers. With the ER algorithm, the belief degrees of each alternative belonging to each linguistic grade are calculated, and then are transformed into two-tuples. The non-linear programming model is constructed according to the distance formula between two two-tuple, and the model is worked out with the improved particle swarm optimization （PSO） algorithm. And a rank of the alternatives is attained. Finally, an example is illustrated to show the feasibility and effectiveness of the method.